# What is the range of the function F(X) = X^2 + 4?

Apr 8, 2017

$y \in \mathbb{R} , y \ge 4$

#### Explanation:

The 'basic' parabola $y = {x}^{2}$ has a $\textcolor{b l u e}{\text{minimum turning point}}$ at the origin (0 ,0)

The parabola $y = {x}^{2} + 4$ has the same graph as $y = {x}^{2}$ but is translated 4 units vertically up and so it's $\textcolor{b l u e}{\text{minimum turning point}}$ is at (0 ,4)
graph{(y-x^2)(y-x^2-4)=0 [-10, 10, -5, 5]}

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ge 4$